Deck 12: Multiple Regression and Model Building

Question 1

Even when an unimportant variable is added to a regression model,the explained variation will increase.

Answer 1

True

Question 2

When the F test is used to test the overall significance of a multiple regression model,if the null hypothesis is rejected,it can be concluded that all of the independent variables x₁,x₂,…x_k are significantly related to the dependent variable y.

Answer 2

False

Question 3

The multiple coefficient of determination can assume any value between 0 and 1,inclusive.

Answer 3

True

Question 4

For the same point estimate of the dependent variable and the same level of significance,the confidence interval is always wider than the corresponding prediction interval.

Question 5

The variance inflation factor measures the relationship between the dependent variable and the rest of the independent variables in the regression model.

Question 6

In a regression equation,beta values are previously known parameter values.

Question 7

For combinations of data within the experimental region,the least squares plane is the estimate of the plane of means.

Question 8

When the quadratic regression model y = $\beta$
0+ $\beta$
1x + $\beta$
2x²+ ? is used,the term $\beta$
1 shows the rate of curvature of the parabola.

Question 9

Testing the contribution of individual independent variables with t-tests is performed prior to the F-test for the model in multiple regression analysis.

Question 10

An outlier may be an incorrectly entered data value.

Question 11

If we increase the number of independent variables in a multiple regression model,the F statistic will always increase.

Question 12

In a regression model,at any given combination of values of the independent variables,the population of potential error terms is assumed to have an F-distribution.

Question 13

A t-test is used in testing the significance of an individual independent variable.

Question 14

Due to the fact that multiple regression models consist of multiple independent variables,residual analysis cannot be performed.

Question 15

The error term in the regression model describes the effects of all factors other than the independent variables on y (response variable).

Question 16

The standard error decreases if and only if the adjusted multiple coefficient of determination decreases.

Question 17

Regression models that employ more than one independent variable are referred to as multiple regression models.

Question 18

An application of the multiple regression model generated the following results involving the F test of the overall regression model: p - value = .0012,R² = .67 and s = .076.Thus,the null hypothesis,which states that none of the independent variables are significantly related to the dependent variable,should be rejected at the .01 level of significance.

Question 19

In a regression model,a value of the error term depends upon other values of the error term.

Question 20

The normal plot is a residual plot that checks the assumption that,for any point in the experimental region,the population of potential error terms is normally distributed.

Question 21

In a multiple regression a very high correlation between predictors would suggest there is an issue of multicollinearity.

Question 22

A researcher in human resources has expressed concern about the differences in job satisfaction results across units within an organization. The researcher conducts a study to investigate what factors could account for the differences. The researcher looked at a random sample of units across the organization and used the factors of percentage of employees with a university degree, the average age of the employees, and the average salary of employees within a unit. The results of the study are presented below:
$\begin{array} { l c l } \text { Predictor } & \text { Coef } & \text { SE Coef } \\ \text { Constant } & 35.178 & 7.595 \\ \text { Degree } & 0.22073 & 0.07131 \\ \text { Age } & 0.3353 & 0.1901 \\ \text { Salary } & 0.0930 & 0.1675 \end{array}$
$s = 7.62090$
Analysis of Variance
$\begin{array} { l c c } \text { Source } & \text { DF } & \text { SS } \\ \text { Regression } & 3 & 1053.09 \\ \text { Residual Error } & 32 & 1858.50\\\\ \text { Source } & \text { DF } & \text { Seq SS } \\ \text { Degree } & 1 & 672.10 \\ \text { Age } & 1 & 363.09 \\ \text { Salary } & 1 & 17.90 \end{array}$

-Using the results above,the value of R² is _____.

A)1053.09
B)0.1790
C)0.1053
D)0.3617
E)2911.59

Question 23

A researcher in human resources has expressed concern about the differences in job satisfaction results across units within an organization. The researcher conducts a study to investigate what factors could account for the differences. The researcher looked at a random sample of units across the organization and used the factors of percentage of employees with a university degree, the average age of the employees, and the average salary of employees within a unit. The results of the study are presented below:
$\begin{array} { l c l } \text { Predictor } & \text { Coef } & \text { SE Coef } \\ \text { Constant } & 35.178 & 7.595 \\ \text { Degree } & 0.22073 & 0.07131 \\ \text { Age } & 0.3353 & 0.1901 \\ \text { Salary } & 0.0930 & 0.1675 \end{array}$
$s = 7.62090$
Analysis of Variance
$\begin{array} { l c c } \text { Source } & \text { DF } & \text { SS } \\ \text { Regression } & 3 & 1053.09 \\ \text { Residual Error } & 32 & 1858.50\\\\ \text { Source } & \text { DF } & \text { Seq SS } \\ \text { Degree } & 1 & 672.10 \\ \text { Age } & 1 & 363.09 \\ \text { Salary } & 1 & 17.90 \end{array}$

-Using the results above,the F statistic would be _____.

A)6.04
B)0.1790
C)3.51
D)0.3617
E)58.08

Question 24

Multicollinearity hinders the regression model's ability to predict the dependent variable on the basis of a combination of values of the independent variable in the experimental region.

Question 25

Which is not an assumption of a multiple regression model?

A)Positive autocorrelation of error terms
B)Normality of error terms
C)Independence of error terms
D)Constant variation of error terms
E)Zero mean of error terms

Question 26

A researcher in human resources has expressed concern about the differences in job satisfaction results across units within an organization. The researcher conducts a study to investigate what factors could account for the differences. The researcher looked at a random sample of units across the organization and used the factors of percentage of employees with a university degree, the average age of the employees, and the average salary of employees within a unit. The results of the study are presented below:
$\begin{array} { l c l } \text { Predictor } & \text { Coef } & \text { SE Coef } \\ \text { Constant } & 35.178 & 7.595 \\ \text { Degree } & 0.22073 & 0.07131 \\ \text { Age } & 0.3353 & 0.1901 \\ \text { Salary } & 0.0930 & 0.1675 \end{array}$
$s = 7.62090$
Analysis of Variance
$\begin{array} { l c c } \text { Source } & \text { DF } & \text { SS } \\ \text { Regression } & 3 & 1053.09 \\ \text { Residual Error } & 32 & 1858.50\\\\ \text { Source } & \text { DF } & \text { Seq SS } \\ \text { Degree } & 1 & 672.10 \\ \text { Age } & 1 & 363.09 \\ \text { Salary } & 1 & 17.90 \end{array}$

-Using the results above,what is the mean square error?

A)32.00
B)58.08
C)372.10
D)1858.50
E)17.90

Question 27

A researcher in human resources has expressed concern about the differences in job satisfaction results across units within an organization. The researcher conducts a study to investigate what factors could account for the differences. The researcher looked at a random sample of units across the organization and used the factors of percentage of employees with a university degree, the average age of the employees, and the average salary of employees within a unit. The results of the study are presented below:
$\begin{array} { l c l } \text { Predictor } & \text { Coef } & \text { SE Coef } \\ \text { Constant } & 35.178 & 7.595 \\ \text { Degree } & 0.22073 & 0.07131 \\ \text { Age } & 0.3353 & 0.1901 \\ \text { Salary } & 0.0930 & 0.1675 \end{array}$
$s = 7.62090$
Analysis of Variance
$\begin{array} { l c c } \text { Source } & \text { DF } & \text { SS } \\ \text { Regression } & 3 & 1053.09 \\ \text { Residual Error } & 32 & 1858.50\\\\ \text { Source } & \text { DF } & \text { Seq SS } \\ \text { Degree } & 1 & 672.10 \\ \text { Age } & 1 & 363.09 \\ \text { Salary } & 1 & 17.90 \end{array}$

-Using the results above,what is the explained variation?

A)1053.09
B)1790.00
C)1858.50
D)3630.90
E)2911.59

Question 28

In comparing regression models,the regression model with the largest R² will also have the smallest standard error (s).

Question 29

The general form of the quadratic multiple regression models is:

A)y = $\beta$ ₁X₁+ $\beta$
₂X₂+ $\varepsilon$
B)y = $\beta$ ₀+ $\beta$
₁X₁+ $\beta$
₂X₂+ $\varepsilon$
C)y = $\beta$ ₀+ $\beta$
₁X + $\beta$
₂X²+ $\varepsilon$
D)y = $\beta$ ₀+ $\beta$
₁X²+ $\varepsilon$
E)y = $\beta$ ₀+ $\beta$
₁X₁+ $\beta$
₂X₂²+ $\varepsilon$

Question 30

The multiple coefficient of determination is the _______ divided by the total variation.

A)unexplained variation
B)SSE
C)explained variation
D)distance value
E)leverage value

Question 31

The assumption of independent error terms in regression analysis is often violated when using time series data.

Question 32

A researcher in human resources has expressed concern about the differences in job satisfaction results across units within an organization. The researcher conducts a study to investigate what factors could account for the differences. The researcher looked at a random sample of units across the organization and used the factors of percentage of employees with a university degree, the average age of the employees, and the average salary of employees within a unit. The results of the study are presented below:
$\begin{array} { l c l } \text { Predictor } & \text { Coef } & \text { SE Coef } \\ \text { Constant } & 35.178 & 7.595 \\ \text { Degree } & 0.22073 & 0.07131 \\ \text { Age } & 0.3353 & 0.1901 \\ \text { Salary } & 0.0930 & 0.1675 \end{array}$
$s = 7.62090$
Analysis of Variance
$\begin{array} { l c c } \text { Source } & \text { DF } & \text { SS } \\ \text { Regression } & 3 & 1053.09 \\ \text { Residual Error } & 32 & 1858.50\\\\ \text { Source } & \text { DF } & \text { Seq SS } \\ \text { Degree } & 1 & 672.10 \\ \text { Age } & 1 & 363.09 \\ \text { Salary } & 1 & 17.90 \end{array}$

-Using the results above,what is the total sum of squares?

A)1053.09
B)1790.00
C)1858.50
D)3630.90
E)2911.59

Question 33

In a multiple regression,the least squares point estimates are values which maximize the sums of squared error.

Question 34

R²is defined as the proportion of the observed variation in the dependent variable that is explained by the fitted regression model.

Question 35

The range of feasible values for the multiple coefficient of determination is from:

A)0 to $\infty$
B)-1 to 0
C)-1 to 1
D)0 to 1
E)- $\infty$ to 0

Question 36

Completely randomized analysis of variance models (one-way ANOVA)can always be converted to a multiple regression models with dummy independent variables.

Question 37

In a multiple regression analysis,if the normal probability plot exhibits approximately a straight line,then it can be concluded that we have not significantly violated the assumption that,for any point in the experimental region,the population of potential error terms is normally distributed.

Question 38

Consider the multiple regression model $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \cdots + \beta _ { k } x _ { k } + \varepsilon$
)When using this model,we assume that at any given combination of values of x₁,x₂,... ,x_k the population of potential error term values has a ________ distribution.

A)binomial
B)normal
C)exponential
D)Poisson
E)logarithmic

Question 39

In multiple regression analysis,if the simple correlation coefficient between the dependent variable and one of the independent variables is .95,then this indicates that the problem of multicollinearity exists.

Question 40

If we are predicting y when the values of the independent variables are x₀₁,x₀₂,…. ,x_0k,the farther the values of x₀₁,x₀₂,…. ,x_0k are from the center of the experimental region,the smaller the distance value and the more precise the associated confidence and prediction intervals.

Question 41

In multiple regression analysis,the explained variation divided by the total variation yields the:

A)Standard error
B)F statistic
C)R²
D)Adjusted R²or $\bar { R } ^ { 2 }$
E)t statistic

Question 42

An investigator hired by a client suing for sex discrimination has developed a multiple regression model for predicting employee salaries for the company in question.In this multiple regression model,the salaries are measured in thousands of dollars.For example,a data entry of 35 for the dependent variable indicates a salary of $35,000.The indicator (dummy)variable for sex is coded as X₁ = 0 if male and X₁ = 1 if female.The computer output of this multiple regression model shows that the coefficient of X₁ is - 4.2 and that X₁ is significant at the 1% level of significance.Interpret the coefficient of X₁.

A)We estimate that,on average,females earn $4200 less than males.
B)We estimate that,on average,males earn $4200 less than females.
C)We estimate that,on average,salaries do not differ.
D)We estimate that,on average,males have 4.2 more years of experience than females.
E)We estimate that,on average,females have 4.2 more years of experience than males.

Question 43

The graph of the prediction equation obtained from fitting the model $\mathrm { y } = \beta _ { 0 } + \beta _ { 1 } X _ { 1 } + \beta _ { 2 } X _ { 2 } + \varepsilon$
Is a(n):

A)Line
B)Plane
C)Parabola
D)Exponential curve
E)Single point

Question 44

Consider the following partial computer output for a multiple regression model.
$$\begin{array}{l}\begin{array} { l l l } \text { Predictor } & \text { Coefficient } \left( \mathrm { b } _ { \mathrm { i } } \right) & \text { Standard Dev } \left( \mathrm { s } _ { \mathrm { b } } \right) \\\text { Constant } & 99.3883 & \\\mathrm { X } 1 & - 0.007207 & 0.0031 \\\mathrm { X } 2 & 0.0011336 & 0.00122 \\\mathrm { X } 3 & 0.9324 & 0.373\end{array}\\\text { Analysis of Variance }\\\begin{array} { l l l } \text { Source } & \text { df } & \text { SS } \\\text { Regression } & 3 & 31.308 \\\text { Error (residual) } & 16 & 9.378\end{array}\end{array}$$

-What is R²?

A)31.308%
B)76.95%
C)87.72%
D)72.63%
E)23.1%

Question 45

Consider the following partial computer output for a multiple regression model.
$$\begin{array}{l}\begin{array} { l l l } \text { Predictor } & \text { Coefficient } \left( \mathrm { b } _ { \mathrm { i } } \right) & \text { Standard Dev } \left( \mathrm { s } _ { \mathrm { b } } \right) \\\text { Constant } & 99.3883 & \\\mathrm { X } 1 & - 0.007207 & 0.0031 \\\mathrm { X } 2 & 0.0011336 & 0.00122 \\\mathrm { X } 3 & 0.9324 & 0.373\end{array}\\\text { Analysis of Variance }\\\begin{array} { l l l } \text { Source } & \text { df } & \text { SS } \\\text { Regression } & 3 & 31.308 \\\text { Error (residual) } & 16 & 9.378\end{array}\end{array}$$

-How many observations were taken?

A)3
B)16
C)19
D)20
E)13

Question 46

If it is desired to include marital status in a multiple regression model by using the categories: single,married,separated,divorced,widowed,what will be the effect on the model?

A)One more independent variable will be included.
B)Two more independent variables will be included.
C)Three more independent variables will be included.
D)Four more independent variables will be included.
E)Five more independent variables will be included.

Question 47

In the interaction model y = β₀+ β₁X₁+ β₂X₂+ β₃X₁X₂+ ε,we would first test the significance of _____.

A)β₃
B)β₂
C)β₁
D)β₀
E)ε

Question 48

The model y = β₀ + β₁x₁ + β₂x₂ + β₃x₁x₂ + ε is a __________.

A)second order polynomial model
B)concave model
C)linear model with interaction
D)convex model
E)quadratic model

Question 49

Consider the following partial computer output for a multiple regression model.
$$\begin{array}{l}\begin{array} { l l l } \text { Predictor } & \text { Coefficient } \left( \mathrm { b } _ { \mathrm { i } } \right) & \text { Standard Dev } \left( \mathrm { s } _ { \mathrm { b } } \right) \\\text { Constant } & 99.3883 & \\\mathrm { X } 1 & - 0.007207 & 0.0031 \\\mathrm { X } 2 & 0.0011336 & 0.00122 \\\mathrm { X } 3 & 0.9324 & 0.373\end{array}\\\text { Analysis of Variance }\\\begin{array} { l l l } \text { Source } & \text { df } & \text { SS } \\\text { Regression } & 3 & 31.308 \\\text { Error (residual) } & 16 & 9.378\end{array}\end{array}$$

-What is the adjusted R²?

A)31.308%
B)76.95%
C)87.72%
D)72.63%
E)23.1%

Question 50

Consider a multiple regression analysis with 20 observations on each of three independent variables and the dependent variable.When performing an overall F test for the model,the critical F value would have ______ numerator degrees of freedom and _______ denominator degrees of freedom.

A)3,17
B)3,16
C)4,16
D)3,19
E)3,20

Question 51

In multiple regression analysis,[explained variation/(k+1)]/MSE yields the:

A)Standard error
B)F statistic
C)R²
D)Adjusted R²or $\bar { R } ^ { 2 }$
E)t statistic

Question 52

For a given multiple regression model with three independent variables,the value of the adjusted multiple coefficient of determination is _________ less than R².

A)always
B)sometimes
C)never

Question 53

In the quadratic regression model,y = $\beta$
₀ + $\beta$
₁X + $\beta$
₂X²+ $\varepsilon$
The ?₂ term represents the:

A)Rate of curvature of the parabola
B)Value of Y when X is zero
C)Shift parameter of the parabola
D)Y-intercept of the parabola
E)Value of X when Y is zero

Question 54

The graph of the prediction equation obtained from fitting the model y = $\beta$
₀+ $\beta$
₁X + $\beta$
₂X²+ $\varepsilon$
Is a(n):

A)Line
B)Plane
C)Parabola
D)Exponential curve
E)Single point

Question 55

A researcher in human resources has expressed concern about the differences in job satisfaction results across units within an organization. The researcher conducts a study to investigate what factors could account for the differences. The researcher looked at a random sample of units across the organization and used the factors of percentage of employees with a university degree, the average age of the employees, and the average salary of employees within a unit. The results of the study are presented below:
$\begin{array} { l c l } \text { Predictor } & \text { Coef } & \text { SE Coef } \\ \text { Constant } & 35.178 & 7.595 \\ \text { Degree } & 0.22073 & 0.07131 \\ \text { Age } & 0.3353 & 0.1901 \\ \text { Salary } & 0.0930 & 0.1675 \end{array}$
$s = 7.62090$
Analysis of Variance
$\begin{array} { l c c } \text { Source } & \text { DF } & \text { SS } \\ \text { Regression } & 3 & 1053.09 \\ \text { Residual Error } & 32 & 1858.50\\\\ \text { Source } & \text { DF } & \text { Seq SS } \\ \text { Degree } & 1 & 672.10 \\ \text { Age } & 1 & 363.09 \\ \text { Salary } & 1 & 17.90 \end{array}$

-Using the results above,what is the number of observations in the sample?

A)6
B)17
C)36
D)32
E)58

Question 56

Based on the multiple regression model given above,if the percentage of employees with a university degree is 50.0,the average age is 43,and the average salary is 48,300 (48.3),the average job satisfaction score is estimated to be _____.

A)65.12
B)17.90
C)36.43
D)68.50
E)58.33

Question 57

Which of the following is not an assumption of the multiple linear regression model?

A)Independent error terms
B)Population of error terms has a normal distribution.
C)Populations of error terms observed at different combinations of values of the independent variable (x₁,x₂,….. ,x_k)have equal variances.
D)The level of measurement of the data for the dependent variable is at least ordinal.
E)At any combination of values of x₁,x₂,….. ,x_k,the population of potential error term values has a mean equal to zero.

Question 58

In the quadratic regression model y = $\beta$
₀ + $\beta$
₁X + $\beta$
₂X²+ $\varepsilon$
The $\beta$
1term represents the:

A)Rate of curvature of the parabola
B)Value of Y when X is zero
C)Value of X when Y is zero
D)Y-intercept of the parabola
E)Shift parameter of the parabola

Question 59

As we increase the number of independent variables in a multiple regression model,the F statistic will _____ increase.

A)always
B)sometimes
C)never

Question 60

In the quadratic regression model y = $\beta$
₀ + $\beta$
₁X + $\beta$
₂ X² + $\varepsilon$
,if the term $\beta$
2 is ______ zero,then the parabola opens __________.

A)less than,upward
B)greater than,upward
C)greater than,either upward or downward
D)less than,either upward or downward
E)equal to,downward

Question 61

Below is a partial multiple regression ANOVA table.
$$\begin{array} { l l l } \text { Source } & \text { SS } & \text { df } \\\mathrm { X } _ { 1 } & 535.9569 & 1 \\\mathrm { X } _ { 2 } & 1,167.5634 & 1 \\\mathrm { X } _ { 3 } & 18.9886 & 1 \\\text { Error } & 3,459.6803 & 8\end{array}$$

-What is the proportion of the variation explained by the multiple regression model?

A).53
B).12
C).18
D).19
E).33

Question 62

Below is a partial multiple regression ANOVA table.
$$\begin{array} { l l l } \text { Source } & \text { SS } & \text { df } \\\mathrm { X } _ { 1 } & 535.9569 & 1 \\\mathrm { X } _ { 2 } & 1,167.5634 & 1 \\\mathrm { X } _ { 3 } & 18.9886 & 1 \\\text { Error } & 3,459.6803 & 8\end{array}$$

-How many observations were in the sample?

A)8
B)10
C)11
D)12
E)14

Question 63

Below is a partial multiple regression ANOVA table.
$$\begin{array} { l l l } \text { Source } & \text { SS } & \text { df } \\\mathrm { X } _ { 1 } & 535.9569 & 1 \\\mathrm { X } _ { 2 } & 1,167.5634 & 1 \\\mathrm { X } _ { 3 } & 18.9886 & 1 \\\text { Error } & 3,459.6803 & 8\end{array}$$

-What is the mean square error?

A)3459.68
B)432.46
C)1898.86
D)1167.56
E)535.96

Question 64

Which of the following residual plots is not used in regression analysis?

A)Residuals vs.parameter estimates
B)Residuals vs.values of an independent variable
C)Residuals vs.time order
D)Residuals vs.predicted values of the dependent variable
E)Standardized residuals vs.predicted values of the dependent variable

Question 65

Which one of the following is not an assumption about the error term in a regression model?

A)Constant variance
B)Independence
C)Normality
D)Variance of zero
E)Mean of zero

Question 66

Below is a partial multiple regression ANOVA table.
$$\begin{array} { l l l } \text { Source } & \text { SS } & \text { df } \\\mathrm { X } _ { 1 } & 535.9569 & 1 \\\mathrm { X } _ { 2 } & 1,167.5634 & 1 \\\mathrm { X } _ { 3 } & 18.9886 & 1 \\\text { Error } & 3,459.6803 & 8\end{array}$$

-What is the value of F?

A)1.28
B)3.28
C)6.22
D)1.33
E)8.11

Question 67

A(n)_____ represents a data point which is unusual with respect to the experimental region and/or which has a y-value which is not consistent with the regression equation.

A)observation
B)correlation
C)distant dot
D)lever
E)outlier

Question 68

An acceptable residual plot exhibits:

A)Increasing error variance
B)Decreasing error variance
C)Constant error variance
D)A curved pattern
E)A mixture of increasing and decreasing error variance

Question 69

In a multiple regression analysis,the least squares prediction equation is computed as $\hat { y }$
= 84.2 + 6.3x₁ - 9.4x₂.If we hold x₂ constant and increase x₁ by 2 units,what is the estimated change in the mean value of y?

A)-18.8
B)-9.4
C)12.6
D)6.3
E)90.5

Question 70

Below is a partial multiple regression ANOVA table.
$$\begin{array} { l l l } \text { Source } & \text { SS } & \text { df } \\\mathrm { X } _ { 1 } & 535.9569 & 1 \\\mathrm { X } _ { 2 } & 1,167.5634 & 1 \\\mathrm { X } _ { 3 } & 18.9886 & 1 \\\text { Error } & 3,459.6803 & 8\end{array}$$

-What is the total degrees of freedom?

A)1
B)3
C)5
D)8
E)11

Question 71

In using a regression model,if a new independent variable is added,the value of the R²(coefficient of multiple determination)will ___________ decrease.

A)always
B)sometimes
C)never

Question 72

As we increase the number of independent variables in a multiple regression model,the F statistic in the analysis of variance table for the multiple regression model will ________ increase.

A)always
B)sometimes
C)never

Question 73

In multiple regression analysis,which one of the following is the appropriate notation for error (residual)?

A) $y _ { i } - \bar { y }$
B) $y _ { i } - \hat { y } _ { i }$
C) $\hat { y } _ { i } - \bar { y }$
D) $\bar { y } - \hat { y } _ { i }$
E)x - y

Question 74

Below is a partial multiple regression ANOVA table.
$$\begin{array} { l l l } \text { Source } & \text { SS } & \text { df } \\\mathrm { X } _ { 1 } & 535.9569 & 1 \\\mathrm { X } _ { 2 } & 1,167.5634 & 1 \\\mathrm { X } _ { 3 } & 18.9886 & 1 \\\text { Error } & 3,459.6803 & 8\end{array}$$

-What is the total sum of squares (total variation)?

A)535.9569
B)1167.5634
C)18.9886
D)3459.68
E)5,182.19

Question 75

In multiple regression analysis,a desirable residual plot has what type of appearance?

A)Curved
B)Cyclical
C)Fanning out
D)Funnelling in
E)Horizontal band

Question 76

Adding any independent variable to a regression model will always increase:

A)Adjusted R²or $\bar { R } ^ { 2 }$
B)s
C)MSE
D)R²
E)The length of all prediction intervals

Question 77

All of the following are desirable outcomes for a multiple regression model except:

A)High R²
B)Large multiple R
C)Small SS residual
D)Large MS residual
E)Large F statistic

Question 78

Below is a partial multiple regression ANOVA table.
$$\begin{array} { l l l } \text { Source } & \text { SS } & \text { df } \\\mathrm { X } _ { 1 } & 535.9569 & 1 \\\mathrm { X } _ { 2 } & 1,167.5634 & 1 \\\mathrm { X } _ { 3 } & 18.9886 & 1 \\\text { Error } & 3,459.6803 & 8\end{array}$$

-What is the explained variation?

A)535.96
B)1,722.51
C)1167.56
D)18.9886
E)3459.68

Question 79

R²is defined as:

A)Total variation/explained variation
B)Explained variation/total variation
C)Unexplained variation/explained variation
D)Total variation/unexplained variation
E)Unexplained variation/total variation

Question 80

Multicollinearity between independent variables is serious when the correlation between pair(s)of dependent variables is _____.

A)close to +/- 1
B)substantially greater than 1
C)zero
D)substantially less than zero